Surely the whole point of Push-ing data to the phone is that it doesn't have to use outgoing data?

In 3G/4G world, there is no "incoming" or "outgoing" data. There is just data, and everything your iPhone does that uses it -- from receiving an email to checking the time and temperature -- uses data when you're not using Wi-Fi. It's a trivial amount most of the time, but it's still using it.